关于实巴拿赫空间中的拟莫比乌斯映射
On quasimöbius maps in real Banach spaces
摘要：
设$E$和$E'$表示维数至少为2的实巴拿赫空间，$D\varsubsetneq E$和$D'\varsubsetneq E'$是整环，$f: D\to D'$是$(M,C)$ -CQH同胚，且$D$是一致的.本文的主要目的是证明$D'$是一致整环当且仅当$f$扩张到同胚$\bar{f}: \bar{D}\to \bar{D}'$且$\bar{f}$是相对于$\partial D$的$η$ -QM.这一结果表明，Väisälä从1991年起提出的一个公开问题的答案是肯定的。
英文摘要：
Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\varsubsetneq E$ and $D'\varsubsetneq E'$ are domains, that $f: D\to D'$ is an $(M,C)$-CQH homeomorphism, and that $D$ is uniform. The main aim of this paper is to prove that $D'$ is a uniform domain if and only if $f$ extends to a homeomorphism $\bar{f}: \bar{D}\to \bar{D}'$ and $\bar{f}$ is $η$-QM relative to $\partial D$. This result shows that the answer to one of the open problems raised by Väisälä from 1991 is affirmative.
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